Suppose $f(z)$ and $g(z)$ are polynomials in $z$, and the degree of $g(z)$ is less than the degree of $f(z)$.  If the degree of $f(z)$ is two, what is the degree of $f(z)+g(z)$?
Solution: We have $f(z)=a_2 \cdot z^2+a_1 \cdot z+a_0$, and $g(z)=b_1 \cdot z+b_0$, where $a_2$ is nonzero.  Then $f(z)+g(z)=a_2 \cdot z^2+(a_1+b_1) \cdot z+(a_0+b_0)$.  The degree of this polynomial is $\boxed{2}$.